Results 161 to 170 of about 243,252 (196)
Some of the next articles are maybe not open access.
Canadian Journal of Mathematics, 1969
The following results (9, Exercise 26, p. 10; 1, Theorem 9.2; 8, Theorem III. 1.11) are known.(A) Let R be a ring with more than one element. Then R is a division ring ifand only if for every a ≠0 in R, there exists a unique b in R such that aba = a.(B) Let R be a near-ring which contains a right identity e ≠ 0.
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The following results (9, Exercise 26, p. 10; 1, Theorem 9.2; 8, Theorem III. 1.11) are known.(A) Let R be a ring with more than one element. Then R is a division ring ifand only if for every a ≠0 in R, there exists a unique b in R such that aba = a.(B) Let R be a near-ring which contains a right identity e ≠ 0.
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Planar Near-Rings, Sandwich Near-Rings and Near-Rings with Right Identity
2005We show that every near-ring containing a multiplicative right identity can be described as a centralizer near-ring with sandwich multiplication. Using this result we characterize planar near-rings and near-rings solving the equation xa=c in terms of such centralizer near-rings with sandwich multiplication.
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1987
The principal theorem states that a finite non-constant near-ring N is geometric if and only if it is strongly monogenic. This provides the basis for a well-defined representation of the group space on the group \(\{Z\to aZ+b| \quad a,b\in N,\quad a\neq 0\}\) acting on the underlying set of N.
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The principal theorem states that a finite non-constant near-ring N is geometric if and only if it is strongly monogenic. This provides the basis for a well-defined representation of the group space on the group \(\{Z\to aZ+b| \quad a,b\in N,\quad a\neq 0\}\) acting on the underlying set of N.
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1997
Not much work has been done on composition near-rings. Here we initiate such investigations. Amongst others we give construction techniques for double composition near-rings and we give two non-isomorphic Peirce decompositions for a composition near-ring (using both the multiplication and composition).
Quentin N. Petersen, Stefan Veldsman
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Not much work has been done on composition near-rings. Here we initiate such investigations. Amongst others we give construction techniques for double composition near-rings and we give two non-isomorphic Peirce decompositions for a composition near-ring (using both the multiplication and composition).
Quentin N. Petersen, Stefan Veldsman
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1992
A near-ring \(N\) is called \(N\)-simple if it has no proper \(N\)-subgroups; it is called \(A\)-simple if it has no \(N\)-subgroups \(H\) such that \(HN=\{0\}\). The radical \(J_ 2(N)\) of a zero-symmetric ring \(N\) with an invariant series whose factors are \(N\)-simple is nilpotent; moreover the factor \(N/J_ 2(N)\) is a direct sum of \(A\)-simple ...
BENINI, Anna, PELLEGRINI, Silvia
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A near-ring \(N\) is called \(N\)-simple if it has no proper \(N\)-subgroups; it is called \(A\)-simple if it has no \(N\)-subgroups \(H\) such that \(HN=\{0\}\). The radical \(J_ 2(N)\) of a zero-symmetric ring \(N\) with an invariant series whose factors are \(N\)-simple is nilpotent; moreover the factor \(N/J_ 2(N)\) is a direct sum of \(A\)-simple ...
BENINI, Anna, PELLEGRINI, Silvia
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1987
Abstract In this paper we introduce a partial order relation in a reduced near-ring and show that the set of all idempotents of a reduced near-ring with identity forms a Boolean algebra under this partial ordering. Further we introduce the notions hyper atom and orthogonal subsets in a reduced near-ring with identity and show that a reduced near-ring
D. Ramakotaiah, V. Sambasivarao
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Abstract In this paper we introduce a partial order relation in a reduced near-ring and show that the set of all idempotents of a reduced near-ring with identity forms a Boolean algebra under this partial ordering. Further we introduce the notions hyper atom and orthogonal subsets in a reduced near-ring with identity and show that a reduced near-ring
D. Ramakotaiah, V. Sambasivarao
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